But only in Design Mode, not when I run my program (by pressing the F5 button).

When i build my project all works fine until I press my custom control (For dragging and selecting). Thats all happening in Design Mode (IDE)
A "X" image is appearing instead of Control's Image, and Visual Studio shows MessageBox with error description. In that description I can read in which line of code error occurs. (ArgumentException occured in file "C:\ ... \BtnEx.vb" line: 67.

When I Build my project (again) the red "X" image dissapears and all loks fine, but as I said, when i click on control that exception occurs.

I know I can do this in other ways, but I want to know why is that happening ?
One of the other ways is to use Me.Width and Me.Height properties of control, but what when i want to use only part of control to draw on it ??

You will get all the log information in the system log where you can examine it using the "Event Log" viewer, using "Eventvwr.msc".

Now, the possible resolution. Design-time can be a disaster, very hard to debug — don't overuse it. Check up the value of the property System.ComponentModel.Component.DesignMode and avoid any extensive or questionable processing if your control methods are executed when the DesignMode is true. Your design mode should only allow to render your control correctly with correct bounds and allow for editing of the properties using the PropertyGrid. All excessive event processing useful only in application execution mode (not design mode) should be avoided.